How do I rig this bridge in Blender?
There are several ways to do this, this is one:



The horizontal bones deform the two platforms, the two vertical bones translate the connecting vertical bars. For the vertical bones, I unchecked inherit rotation in the bone tab.
The bottom green bone copies rotations of the top right bone. This is the control bone for the whole setup, you could hide all other bones.

Take a look at the blend: